Zobrazeno 1 - 10
of 528
pro vyhledávání: '"65d20"'
Autor:
Finch, Steven
N. G. de Bruijn (1958) studied the asymptotic expansion of iterates of sin$(x)$ with $0 < x \leq \pi/2$. Bencherif & Robin (1994) generalized this result to increasing analytic functions $f(x)$ with an attractive fixed point at 0 and $x > 0$ suitably
Externí odkaz:
http://arxiv.org/abs/2411.01591
Autor:
Finch, Steven
We treat three recurrences involving square roots, the first of which arises from an infinite simple radical expansion for the Golden mean, whose precise convergence rate was made famous by Richard Bruce Paris in 1987. A never-before-seen proof of an
Externí odkaz:
http://arxiv.org/abs/2410.02114
Autor:
Bernatska, Julia
Numerical tools for computation of $\wp$-functions, also known as Kleinian, or multiply periodic, are proposed. In this connection, computation of periods of the both first and second kinds is reconsidered. An analytical approach to constructing the
Externí odkaz:
http://arxiv.org/abs/2407.05632
Autor:
Bakhvalov, Pavel
We consider the 2D acoustic system with the Gaussian pulse as the initial data. This case was proposed at the first Workshop on benchmark problems in computational aeroacoustics, and it is commonly used for the verification of numerical methods. We c
Externí odkaz:
http://arxiv.org/abs/2404.10489
Publikováno v:
SIGMA 20 (2024), 075, 9 pages
We derive asymptotic expansions of the large zeros of the Coulomb wave functions and for those of their derivatives. The new expansions have the same form as the McMahon expansions of the zeros of the Bessel functions and reduce to them when a parame
Externí odkaz:
http://arxiv.org/abs/2402.14537
We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel functions and their derivatives in terms of inverse values of some ele
Externí odkaz:
http://arxiv.org/abs/2402.06956
Autor:
Miyamoto, Roland
The iterates $h_0,h_1,h_2,\dotsc$ constructed in [8,5] and converging to the only solution $g=h\colon[0,1]\to[0,1]$ of the iterative differential equation $-\gamma g'= g^{-1}$, $\gamma>0$, are parametrised by polynomials over $\Bbb Q$, and the corres
Externí odkaz:
http://arxiv.org/abs/2402.06618
Autor:
Straton, Jack C.
The Bessel function of the first kind $J_{N}\left(kx\right)$ is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind $I_{N}\left(kx\right)$. The purpose of these expansions in Legendre polynomials was not an at
Externí odkaz:
http://arxiv.org/abs/2401.08597
This paper develops a constructive numerical scheme for Fourier-Bessel approximations on disks compatible with convolutions supported on disks. We address accurate finite Fourier-Bessel transforms (FFBT) and inverse finite Fourier-Bessel transforms (
Externí odkaz:
http://arxiv.org/abs/2311.03772
Autor:
Schmid, Harald
Publikováno v:
Mathematics and Computers in Simulation, 2024
This paper is concerned with the connection coefficients between the local fundamental solutions of a $2\times 2$ linear ordinary differential system with two neighboring regular singular points at $z=0$ and $z=1$. We derive an asymptotic formula for
Externí odkaz:
http://arxiv.org/abs/2308.06511